Person in Charge

• 035966_L3

Problem Description

struct S
{
	bool c[5012];
	int dc[5012][2];
	int ts = 1;
	int x;
	void init(int h)
	{
		memset(c, 0, sizeof c);
		memset(dc, 0, sizeof dc);
		c[1] = 0;
		ts = 1;
		x = h;
	}
	void add(int num)
	{
		int now = 1;
		for (int i = 1, j = x; j >= 0; i++, j--)
		{
			bool cc = num & (1 << j);
			int xx = ts + 1;
			if (dc[now][cc]) xx = dc[now][cc];
			if (xx > ts)
			{
				ts++;
				dc[now][cc] = ts;
				c[ts] = cc;
			}
			now = xx;
		}
	}
};

The above code implements a 01 Trie.

This 01 Trie can store any integer in the range $[0,2^x)$ via the add function. After insertion, the value of variable ts reflects the actual space used by this 01 Trie.

Your task is to insert $y$ integers from $[0,2^x)$ into such a 01 Trie to maximize its actual space usage.

Input Format

Each test consists of multiple test cases.

The first line contains a positive integer $T$, indicating the number of test cases.

Each of the next $T$ lines contains two positive integers $x$ and $y$.

Output Format

For each test case, output one line containing $y$ integers from $[0,2^x)$, representing the integers you insert.

Samples

6
1 1
1 2
2 1
2 2
2 3
2 4

1
0 1
0
1 2
3 0 1
2 3 0 1

Sample Explanation

The ts values for the 6 test cases are $2,3,3,5,6,7$ respectively.

Note: The solution is not unique.

Data Range

$1 \le T \le 2046, 1 \le x \le 10, 1 \le y \le 2^x.$